26 citations · 77 across the 15 of their papers we have counts for
16 papers
2-roots for simply laced Weyl groups
R. M. Green, Tianyuan Xu
We introduce and study "2-roots", which are symmetrized tensor products of orthogonal roots of Kac--Moody algebras. We concentrate on the case where is the Weyl group of a simp…
On Limit Measures and Their Supports for Stochastic Ordinary Differential Equations
Tianyuan Xu, Lifeng Chen, Jifa Jiang
This paper studies limit measures of stationary measures of stochastic ordinary differential equations on the Euclidean space and tries to determine which invariant measures of an…
Kazhdan--Lusztig cells of -value 2 in -finite Coxeter systems
R. M. Green, Tianyuan Xu
A Coxeter group is said to be \emph{-finite} if it has finitely many elements of -value 2 in the sense of Lusztig. In this paper, we give explicit combin…
Critical Sharp Front for Doubly Nonlinear Degenerate Diffusion Equations with Time Delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
This paper is concerned with the critical sharp traveling wave for doubly nonlinear diffusion equation with time delay, where the doubly nonlinear degenerate diffusion is defined b…
Subregular -rings of Coxeter systems via quiver path algebras
Ivan Dimitrov, Charles Paquette, David Wehlau +1
We study the subregular -ring of a Coxeter system , a subring of Lusztig's -ring. We prove that is isomorphic to a quotient of the path algebra of the doub…
Propagation speed of degenerate diffusion equations with time delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
We are concerned with a class of degenerate diffusion equations with time delay describing population dynamics with age structure. In our recent study [{\em Nonlinearity}, 33 (2020…
A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion
Shanming Ji, Zhian Wang, Tianyuan Xu +1
This paper is concerned with traveling wave solutions for a chemotaxis model with degenerate diffusion of porous medium type. We establish the existence of semi-finite traveling wa…
Variational Approach of Critical Sharp Front Speeds in Density-dependent Diffusion Model with Time Delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
For the classical reaction diffusion equation, the priori speed of fronts is determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier, {\em Commun. Math. Phys.}…
Sharp, Smooth, and Oscillatory Traveling Waves of Degenerate Diffusion Equation with Delay
Tianyuan Xu, Shanming Ji, Ming Mei +1
We consider the non-monotone degenerate diffusion equation with time delay. Different from the linear diffusion equation, the degenerate equation allows for semi-compactly supporte…
Theoretical and numerical studies on global stability of traveling waves with oscillations for time-delayed nonlocal dispersion equations
Tianyuan Xu, Shanming Ji, Rui Huang +2
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically…
Propagating Profiles of a Chemotaxis Model with Degenerate Diffusion: Initial Shrinking, Eventual Smoothness and Expanding
Tianyuan Xu, Shanming Ji, Ming Mei +1
We investigate the propagating profiles of a degenerate chemotaxis model describing the bacteria chemotaxis and consumption of oxygen by aerobic bacteria, in particular, the effect…
Classification of Coxeter groups with finitely many elements of -value 2
R. M. Green, Tianyuan Xu
We consider Lusztig's -function on Coxeter groups (in the equal parameter case) and classify all Coxeter groups with finitely many elements of -value 2 in t…
Early and late stage profiles for a new chemotaxis model with density-dependent jump probability and quorum-sensing mechanisms
Tianyuan Xu, Shanming Ji, Chunhua Jin +2
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migrati…
On the subregular -rings of Coxeter systems
Tianyuan Xu
We recall Lusztig's construction of the asymptotic Hecke algebra of a Coxeter system via the Kazhdan--Lusztig basis of the corresponding Hecke algebra. The algebra …
Sandpiles and Dominos
Laura Florescu, Daniela Morar, David Perkinson +2
We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axe…
A Note on the Critical Group of a Line Graph
David Perkinson, Nicholas Salter, Tianyuan Xu
This note answers a question posed by Levine in arkiv:math.CO/0906.2809. The main result is Theorem 1 which shows that under certain circumstances a critical group of a directed gr…